Gemara

"Gedilim" teaches the number of threads. 'Gedil' is (threads wrapped together, i.e. at least) two. "Gedilim" (plural) is four;

The Torah says to make a Gedil (wrap them together) and 'Poslehu' (this will be explained).

Menachos 41b (Beraisa #1 - Beis Shamai): Four threads are required (they are put through the corner and doubled over, making eight ends). Four (Tefachim) must be Meshuleshes (this will be explained);

Beis Hillel require three threads (six ends). Three must be Meshuleshes.

(Rav Huna): Four threads are required.

(Rav Yehudah): Three threads are required.

(Rav Papa): The Halachah requires four threads

Inference: The Beraisa implies that there is a Shi'ur of Tzitzis.

Contradiction (Beraisa #2): Tzitzis must extend somewhat past the corner. Mashehu (any amount) is Kosher;

Elders of Beis Hillel and Beis Shamai: There is no Shi'ur of Tzitzis. Similarly, there is no Shi'ur of a Lulav.

Suggestion: This means that there is no Shi'ur at all!

Answer: No, it means that there is no upper Shi'ur, but there is a minimal Shi'ur

39a (Rabah bar bar Chanah): The thread wrapped around the others counts towards the required number of threads.

42a: Rav Acha bar Yakov folded four threads, and put the folded ends through the corner. He then put the two ends of each thread through the loop in its middle;

He requires eight threads through the garment itself, to fulfill Gedilim (four threads) where there is Pesil.

R. Yirmeyah mi'Difti folded eight threads, and put the folded ends through the corner. He did not put the 16 ends through the loops.

Mar brei d'Ravina did like we do (he put four unfolded threads through the corner).

Sanhedrin 88a (R. Elazar): A Zaken Mamre is liable also for a Mitzvah whose source is explicit in the Torah, and is explained by Chachamim, if it is possible (but forbidden) to add to the law, and by doing so he invalidates it. The only such example is Tefilin.

Question: The source of Tzitzis is explicit in the Torah and it is explained by Chachamim. If one adds additional threads he invalidates the Mitzvah!

Answer: If we hold that the Torah does not require tying the threads even once (after inserting them through a hole in the corner), the extra threads do not invalidate the Mitzvah;

If we hold that the Torah requires tying the threads, it was invalid from the beginning (he tied too many threads)!

Rishonim

Rif and Rosh (Hilchos Tzitzis (after Menachos) 12a and Siman 6): The Halachah requires four threads. The thread wrapped around the seven counts towards the eight required.

Rosh: This connotes that the windings and Anaf (straight part) together are four. Rashi says that the Anaf alone is four, so altogether it is six. R. Tam says that the Gedil alone is four. This is like the Sifri. It says that "V'Osu Lahem Tzitzis" teaches only one. The Halachah follows Beis Shamai, who learn from "Gedilim Ta'aseh Lach" that we need four threads of Lavan and four of Techeiles, and they must be four fingers. Since this was expounded regarding Gedilim, it itself must be four, so the entire length is 12.

Rambam (Hilchos Tzitzis 1:1): The Torah requires us to put on the corners Anaf (straight threads,) like hairs. It is called Lavan because we need not dye it. The Torah does not specify the number of threads.

Kesef Mishneh: The Rambam proceeds to say how many threads are required. He means that the number is not explicit in the Torah. Rav Acha and R. Yirmeyah argue about the number. If one has too many, he transgresses Bal Tosif (Sanhedrin 88a). The Halachah follows Rav Acha, for Rav Papa concludes that four threads are required. However, the Gemara in Yevamos (5b) connotes that the Torah explicitly requires four! This requires investigation.

Rambam (6): One inserts four threads through the corner and bends them in the middle, making eight threads Meshulashim. Their length must be at least four fingers; it can be very long. One of the eight threads is Techeiles, and the other seven are Lavan.

Rebuttal (Ra'avad): Two of the eight are Techeiles, and the other six are Lavan.

Kesef Mishneh: The Rambam learns from the singular "Pesil". The Sifri supports him.

Rambam (9): One who puts Lavan threads without Techeiles takes one of the eight threads and wraps it around the others.

Rosh (Siman 6): Rashi says that the Mitzvah is to have two threads of Lavan and two of Techeiles. The Mishnah teaches that they are not Me'akev each other, and all four can be of either. Seemingly 'are not Me'akev each other' connotes that it suffices to have just two of one kind, like we say that Tefilin Shel Rosh and Shel Yad are not Me'akev each other (one may wear one without compensation for the lack of the other). The custom is like Rashi. He is supported by the Gemara that says that one who puts (wool) Kala Ilan in place of Techeiles does not transgress, even if the garment is linen. However, perhaps the Drashah from "Gedilim" requires four threads, but there is no upper limit; whatever one puts is a Mitzvah and overrides Sha'atnez. Similarly, "Arvei Nachal" teaches that two are required, yet our custom is to put many with the Lulav. 'There is no Shi'ur' refers to both the length and number of Tzitzis. One who has too many threads transgresses Bal Tosif. Perhaps this is only if he puts more than eight. We find that Amora'im put between four and eight; no one transgressed. Where does the Torah allude to this? It says "...Tzemer u'Fishtim Yachdav; Gedilim Ta'aseh Lach" to teach that the four threads (Gedilim) may comprised of two wool (Techeiles) and two linen (Lavan), or one may have four of each.

Poskim

Shulchan Aruch (OC 11:12): Each corner must have four doubled threads, making eight. If one has more it is Pasul. One cuts the ends of the four threads (i.e. if he starts with one long thread) and inserts them through the corner and bends them, and then they are eight.

Beis Yosef (DH v'Chosav): The Ba'al ha'Itur says that there is no upper limit to the number or threads. Presumably he learns from Rav Acha and R. Yirmeyah, who doubled the threads after inserting them. 'There is no Shi'ur' refers to both the length and number of Tzitzis.

Beis Yosef (DH v'Nir'eh): The Ri allows up to eight doubled threads, i.e. up to four each of Techeiles and Lavan. Nowadays that we do not have Techeiles, up to four are allowed. One could explain that nowadays eight Lavan are allowed, but the first way is primary.

Beis Yosef (DH veha'Rambam): The Nimukei Yosef (Reish 12b) says that there is a tradition for the number of threads. One should have exactly 32 (in all, for the four corners) after they are folded.

Gra (DH Minyan): The Halachah follows Beis Shamai, who require four threads, i.e. two doubled threads, of Lavan and similarly of Techeiles. Nowadays we put two extra doubled Lavan threads (four in all) in place of the Techeiles.

Mishnah Berurah (59): The Gra and others rule like the Ba'al ha'Itur, that extra threads are not Posel. One transgresses Bal Tosif only if he adds something different, like we say regarding Lulav. If one has too many threads, he may rely on their opinion to wear the garment until he can fix it. All agree that too few threads is Pasul.

Mishnah Berurah (61): It is l'Chatchilah to cut the ends of the threads before inserting them through the corner. One should not cut them with a knife, rather, with his teeth.

Shulchan Aruch (13): One must be careful to cut the ends to make them eight before winding them. If he winds even one Chulyah (the part between knots) and tied the knot and then cut them it is Pasul due to Ta'aseh v'Lo Min ha'Asuy, i.e. it was Pasul when it was done.

Magen Avraham (19, according to Eshel Avraham): Olas Tamid disqualifies if they were not cut before winding or tying. This is wrong; winding by itself is insignificant.

Kaf ha'Chayim (40): Perhaps one should insert all four threads together. If he inserts one it is Pasul at the time, and when he inserts the others this is Ta'aseh v'Lo Min ha'Asuy. However, b'Di'eved it is Kosher, for even if they were cut after they were inserted it is Kosher.